Finding Singular Features
This addresses the challenge of detecting unexpected or unknown hidden structures in data for applications like data analysis and pattern recognition, representing a domain-specific incremental improvement.
The paper tackles the problem of identifying high-density, low-dimensional structures, termed 'singular features', in noisy point clouds, and presents a method that outputs well-defined sets of dimensions d<D, showing effectiveness in noisy conditions unlike spectral clustering.
We present a method for finding high density, low-dimensional structures in noisy point clouds. These structures are sets with zero Lebesgue measure with respect to the $D$-dimensional ambient space and belong to a $d<D$ dimensional space. We call them "singular features." Hunting for singular features corresponds to finding unexpected or unknown structures hidden in point clouds belonging to $\R^D$. Our method outputs well defined sets of dimensions $d<D$. Unlike spectral clustering, the method works well in the presence of noise. We show how to find singular features by first finding ridges in the estimated density, followed by a filtering step based on the eigenvalues of the Hessian of the density.